Demonstrators hold signs at Hartsfield-Jackson International Airport during a demonstration to denounce President Donald Trump’s executive order on immigration. Photo / AP

The White House tried to tamp down concerns about President Donald Trump’s sweeping immigration order in the face of widespread protests, as some Republicans in Congress urged him to proceed with caution in the face of legal pushback.

Top congressional Republicans, however, remain largely behind the new president.

During a round of show interviews, Trump’s aides stressed that just a small portion of travellers had been affected by the order, which temporarily bars the citizens of seven majority Muslim nations from entering the country.

The aides also reversed course and said that citizens of those countries who hold permanent US residency “green cards” will not be barred from re-entering the US, as officials had previously said.

“I can’t imagine too many people out there watching this right now think it’s unreasonable to ask a few more questions from someone travelling in and out of Libya and Yemen before being let loose in the United States,” said Trump’s chief of staff Reince Priebus.

As of today, one legal permanent resident had been denied entry to the country as a result of the order, according to a federal law enforcement official.”And that’s all this is.”

Homeland Security Secretary John Kelly issued a statement saying he deemed the entry of lawful permanent residents to be in the national interest, and absent information indicating a serious threat to public safety and welfare, residency would be a “dispositive factor in our case-by-case determination”.

The changes, said White House adviser Kellyanne Conway, are “a small price to pay” to keep the nation safe.

But it’s unclear whether the order, which also suspends refugee admissions for 120 days and indefinitely bars the processing of refugees from Syria, will accomplish that.

The order does not address homegrown extremists already in America, a primary concern of federal law enforcement officials. And the list of countries in Trump’s order doesn’t include Saudi Arabia, where most of the September 11 hijackers were from.

Priebus said that other countries could be added to the list.

Trump spoke by phone Sunday with leaders from Saudi Arabia and the United Arab Emirates, two countries not affected by the change.

The order has sparked widespread protests and denunciations from Democrats and a handful of Republicans. Many have accused the administration of rushing to implement the changes, resulting in panic and confusion at the nation’s airports.